New formulae for efficient elliptic curve arithmetic

被引：0
|
作者：
Hisil, Huseyin [1 ]
Carter, Gary [1 ]
Dawson, Ed [1 ]
机构：
[1] Queensland Univ Technol, Informat Secur Inst, Brisbane, Qld, Australia
来源：
PROGRESS IN CRYPTOLOGY - INDOCRYPT 2007 | 2007年 / 4859卷
关键词：
elliptic curve; efficient point multiplication; doubling; tripling; DBNS;
D O I：
暂无
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
This paper is on efficient implementation techniques of Elliptic Curve Cryptography. In particular, we improve timings' for Jacobi-quartic (3M+4S) and Hessian (7M+1S or 3M+6S) doubling operations. We provide a faster mixed-addition (7M+3S+1d) on modified Jacobi-quartic coordinates. We introduce tripling formulae for Jacobi-quartic (4M+11S+2d), Jacobi-intersection (4M+10S+5d or 7M+7S+3d), Edwards (9M+4S) and Hessian (8M+6S+1d) forms. We show that Hessian tripling costs 6M+4C+1d for Hessian curves defined over a field of characteristic 3. We discuss an alternative way of choosing the base point in successive squaring based scalar multiplication algorithms. Using this technique, we improve the latest mixed-addition formulae for Jacobi-intersection (10M+2S+1d), Hessian (5M+6S) and Edwards (9M+1S+ 1d+4a) forms. We discuss the significance of these optimizations for elliptic curve cryptography.
引用
收藏
页码：138 / 151
页数：14
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